Hyperbolicity of generic hypersurfaces of polynomial degree via Green-Griffiths jet differentials

We give a new version of a recent result of B{é}rczi-Kirwan, proving the Kobayashi and Green-Griffiths-Lang conjectures for generic hypersurfaces in the projective space , with a polynomial lower bound on the degree. Our strategy again relies on Siu’s technique of slanted vector fields and the use of holomorphic Morse inequalities to prove the existence of a jet differential equation with a negative twist – however, instead of using a space of invariant jet differentials, we base our computations on the classical Green-Griffiths jet spaces.